J. Am. Chem. SOC.1992, 114, 7727-7736
7121
Autoxidation of Alkylnaphthalenes. 2. Inhibition of the Autoxidation of n-Hexadecane at 160 O C 1 J. Igarashi,2 R. K. Jensen,j J. Lusztyk,* S. Korcek,j and K. U. Ingold Contribution from the Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, Canada K I A OR6, and Research Staff. Ford Motor Company, Dearborn. Michigan 481 21. Received January 10, I992
Abstract: The rate of the self-initiated autoxidation of hexadecane at 160 OC under 760 Torr of O2is reduced by the addition of submolar concentrations of naphthalene or alkylnaphthalene. The kinetics of these (alkyl)naphthalenemodulated,self-initiated hexadecane autoxidations have been examined by monitoring hydroperoxide concentrations. Under similar conditions, the extent of the rate retardation is essentially identical for equal concentrations of naphthalene and 1- and 2-methylnaphthalene (and 2-sec-butylnaphthalene), which proves that retardation is due to chemistry associated with the naphthalene moiety. It is shown that the (alky1)naphthalene produces both an increase in the rate constant for a bimolecular, peroxyl + peroxyl chain-termination process and a kinetically-first-order chain-termination reaction. Both of these termination processes are attributed to an initial addition of hexadecylperoxyl radicals to the naphthalene ring. Reaction of the resultant peroxycyclohexadienyl radical with O2produces the HOO' radical which is responsible for the increase in the rate constant for bimolecular termination. Unimolecular decomposition of the peroxycyclohexadienyl radical yields hexadecanol and an (a1kyl)naphthoxyl radical, the latter being responsible for the kinetically-first-order termination process. A simplified scheme of 17 elementary reactions yields a kinetic expression which, via computer modeling, is shown to give a very satisfactory agreement between calculated and measured hydroperoxide yields under all experimental conditions surveyed. This simulation yields a rate constant k19of -70 M-' s-l for the addition of hexadecylperoxyl radicals to (alky1)naphthalenes at 160 O C , a value which may be compared with the estimated rate constant for hydrogen abstraction from 1- or 2-methylnaphthalene under similar conditions, viz., k l s = 34 M-'s-l. The simulation also gives a satisfactory agreement between calculated and measured yields of organic hydroperoxides and hydrogen peroxide. That the naphthalene ring was oxidatively cleaved under the experimental conditions was demonstrated by the identification of phthalic acid and phthalic anhydride following the addition of naphthalene or a methylnaphthalene to autoxidizing hexadecane. Both 1- and 2methylnaphthalene also yielded 2-acetylbenzoic acid. The possible mechanisms by which these naphthalene ring-cleaved products are formed are discussed.
In the preceding paper4 we demonstrated that the unexpectedly high resistance to autoxidation of 1- and 2-methylnaphthalene at temperatures from 30 to 60 OC is due to a combination of autoretardation and self-inhibition. The former effect can be attributed to the buildup of molecular oxidation products which can function as chain-breaking antioxidants. The latter effect was attributed to the addition of peroxyl radicals to the naphthalene ring which leads to chain-breaking by a kineticallyfirst-order chain-termination process. This addition reaction accompanies H-atom abstraction from the methyl group so that even the very initial stages of the autoxidation are inhibited. In this paper we extend our kinetic studies to higher temperatures where the unusual resistance to autoxidation of alkylnaphthalenes has already been demonstrated>6 a resistance which makes these compounds attractive as synthetic lubricating oils and heat transfer fluids. Specifically, we have examined the effect of the two methylnaphthalenes and of naphthalene itself (and of 2-see-butylnaphthalene) on the rates of the self-initiated autoxidation of hexadecane a t 160 O C . The results obtained are readily explained within the general framework of the reactions invoked at lower temperature^.^
Self-InitiatedAutoxidationof Hexadecane at 160 "C. Extensive studies by some of the present authors7-I3 have demonstrated that the autoxidation of hexadecane, C16H34r at 160 O C occurs 'spontaneously" with chain-initiation W i g due to the unimolecular thermal decomposition of isomeric hexadecyl mono- and dihydroperoxides, -00H.I4J5 The overall autoxidation process at relatively low extents of oxidation is shown in simplified formI6 in Scheme I. The various organic species shown in this scheme correspond, of course, to mixtures of isomers. Application of the usual steady-state approximations to Scheme Address correspondence to this author at the National Research Council of Canada.
0002-7863/92/ 15 14-7727$03.00/0
(2kS[C16H341 + k7)[HOOC16H3200'1 (1) (1) Issued as NRCC No. 33306. (2) On leave from the Nippon Oil Company, Japan. (3) Ford Motor Company. (4) Igarashi, J.; Lusztyk, J.; Ingold, K. U. Preceding paper in this issue. (5) Larsen, R. G.; Thorpe, R. E.; Armfield, F. A. Ind. Eng. Chem. 1942, 34, 183-193. (6) Yoshida, T.; Watanabe, H. US.Patent 4,714,794, December 22, 1987. (7) Jensen, R. K.; Korcek, S.;Mahoney, L. R.; Zinbo, M. J . Am. Chcm. SOC.1979, 101, 7574-7584.
Published 1992 by the American Chemical Society
7728 J. Am. Chem. SOC.,Vol. 114, No. 20, 1992 We now assume that k4 = k5 = k, and hence
E
0.2 -
I
OS3l
t
I/ 0.0
c
' " ' 1 " " ' ' " 1 " " ~ " " ' '
0
2000
Time
where
4 = 1 + +(2
+ e)/(l + +)
(VW
In eqs VI and VI1 the dimensionless parameter 4 reflects the increased rate of formation of hydroperoxides due to the production of difunctional oxidation products. The magnitude of 4 depends on the hexadecane and oxygen concentration^'^ and on the magnitude of various rate constants.I8 4 is always greater than (8) Jensen, R. K.; Korcek, S.;Mahoney, L. R.; Zinbo, M. J . Am. Chem. SOC.1981, 103, 1742-1749.
(9) Korcek, S.;Mahoney, L. R.; Jensen, R. K.; Zinbo, M.; Willermet, P. A.; Kandah, S. K. Report 1983, AFOSR-TR-83-0987; Order No. ADA135464, 214 pp. (10) Korcek, S.; Jensen, R. K.; Zinbo, M.;Mahoney, L. R. PREPRINTS, Diu.Petrol. Chem.. Am. Chem. SOC.1987. 32. 833-840. (1 1) Zinbo, M.;Jensen, R. K.; Johnson, M. D.; Korcek, S.Id.Eng. Chem. Res. 1987. 26. 902-906. (12) Jensen, R. K.; Johnson, M. D.; Korcek, S.;Zinbo, M. Int. J . Chem. Kinet. 1990, 22, 1095-1 107 (13) Jensen, R.K.; Korcek, S.;Zinbo, M. Unpublished results. (14) -OOH represents the totality of hydroperoxides produced during autoxidation. (15) "Spontaneous" initiation at the start of each experiment may be due + to a combination of a direct reaction between oxygen and hexadecane (02 C16H34 HOO' + cl6H33'), thermal decomposition of -OOH present at concentrations too low to detect, and background y and cosmic ray events. (16) Reaction 6 involves both a,y- and a,S-intramolecular H-atom abstractions. Reaction 7 involves intramolecular a , y - and @,&abstractionof the tertiary H-atom from the -CH2CH(OOH)CHz- moiety to form the -CH,C'(OOH)CH2- radical which undergoes immediate ,%scission. A more comprehensive schemelo*" would include reaction 6': 1~
I
/
4000
6000
s
Figure 1. Plot of [hydroper~xide]''~ vs time for the self-initiated autoxidation of hexadecane at 160 O C under 760 Torr of 02:no additives (m); with additives, 1-methylnaphthalene, 0.31 M, (a), 2-methylnaphthalene, 0.28 M (A),naphthalene, 0.30 M (+), BMP, 1.2 X lo-' M ( O ) , 1-methylnaphthalene, 0.31 M, and BMP, 1.2 X M (0). All additivas indicated above were introduced into autoxidizing hexadecane at lo = 620 s, [-OOH],, = 0.01 M. The smooth, thick curve has been computed for the 1-methylnaphthalene modulated autoxidation of hexadecane as described in the text.
unity (4 > 1.0). At a given oxygen pressure and at low conversions where [C16H34]remains approximately constant, 4 is also a con~tant.~~-~~ In a stirred-flow reactor eq VI has been shown to be obeyed during the early stages of hexadecane a u t o ~ i d a t i o n . ' * ~For ~J~ application to batch reactions, eq VI can be integrated from the start of the experiment at a time t = to to the time t at which the measurement of the -OOH concentration has been made:
~
where
-.
a,b-HOOCl6H32'
-
CH~(CH~),CHCHZCH~CH(CH~)I(~CH, + HO' (6')
'02
and the thermal decomposition of the relatively unstable O=C.CIsH3100H. (17) As previously defined:10J3*16 $=
kp 1 kp[C16Hd + 6'' 1 + h7/k3[021
w
kp[C1&341
+ 1 (A) kT6 1 + (h6k6')/k3[021
At high oxygen pressures where all the HOOC16H32' radicals are captured by O2 (reaction 3) equation A simplifies to:
(18) For the autoxidation of hexadecane at 160 'C the following rate constants have been determined using a stirred-flow r e a ~ t o r : ~ ki ~ J=~2.82 *~~ X l(Ts s-', k = 88.9 M-I C', = 83.6 s-l, = 6.28 X 10's-I, = 1225 s-l, = 55.6 s-l, k$ = 1.05 X los s-l, e6 = 339 s-l, k6, (see footnote 16) = 1.7 X lo4 S-I. It is assumed that k3 = 1 X lo9 M-I s-l. (19) Jensen, R. K. Unpublished results.
e'
e7
w7
A plot of [-OOH]f1/2versus t for the self-initiated autoxidation of neat hexadecane (2.98 M) a t 160 OC and 760 Torr of O2 in a batch reactor is indeed linear (as predicted by eq X)during the early stages of the reaction (see filled squares and the straight line going through the origin in Figure 1). The slope of this line yields K = 4.91 x 10-5 M-112 s-112 Using kinetic information which is we can calculate22 that 4 = 1.40 under these experimental conditions and hence M-lf2 s-l12 kp(2ki/2k,)'/2 = 7.03 X ~~
(20) The value of k (388.9 M-I
was calculated from the slope of a plot of d[C16H3300Hf/dt versus [-00H]1/2, this slope bein equal to kp[c16H,4](2k,/2k,)1/2/(1+ 4' )'. Thevalues of ki= 2.82 X lO-?s-l and 2k, = 1.12 X 10' M-I s'I used in deriving kp were obtained from the Arrhenius parameters given for the relevant reactions in refs 12 and 21, respectively. (21) Bennett, J. E.; Eyre, J. A,; Summers, R. J . Chem. Sm., Perkin Trans. 2 1974, 797-800. (22) The magnitude of 4 can be calculated from eqs VII, IV,and AI' or B.I7 The values of the rate constants used for this calculation at 160 OC are given in footnote 18. The concentration of O2 was estimated from oxygen solubility data as equal to 2.65 X lo-' M at 760 Torr of 02.23 (23) Jensen, R. K.; Korcek, S.;Zinbo, M. Oxid. Commun. 1990, 13, 258-262. (24) Boozer, C. E.; Hammond, G. S.; Hamilton, C. E.; Sen, J. N. J . Am. Chem. SOC.1955, 77, 3233-3247. s-I)
Autoxidation of Alkylnaphthalenes. 2
J . Am. Chem. Soc.. Vol. 114, No. 20, 1992 7729
The value of ki can be derived using the "induction period method".'2v24 Thus, the addition of 1.2 X M 2,6-di-tertbutyl-4-methylphenol (BMP) to autoxidizing hexadecane at to = 620 s (corresponding to [-OOH]'/2 = 0.1 Le., to [-OOH] = 0.01 M)25completely prevented further oxidation for a period of 2555 s, after which time the oxidation rate returned to approximately its original value (seeopen squares in Figure 1). From the duration of this induction period it is poasible to calculate the At lower rate of chain initiation, Ri, by ca. 0.01 M [-OH]. , I temperatures BMP traps 2.0 peroxyl radicals per m o l e c ~ l e , ~ ~ ~ ~ ~ T v but at 160 "C it traps an average of only 1.2 peroxyl radicals per mole~ule.~ Hence, Ri= 1.2 X (1.2 X 10-3)/2555 = 5.64 X lo-' P s-' M-' s-' at [+OH] = 0.01 M. Therefore, ki = 2.82 X and kp/(2k,)1/2= 0.94 X lo-, M-II2 sW1I2, values which are in \ , >, , , , I 0 2000 4000 6000 satisfactory agreement with 2.5 X s-' and 0.93 X M-'i2 s-'12, respectively, reported previously at this t e m p e r a t ~ r e . ' ~ . ' ~ Time / s We also measured the rate of hydroperoxide formation at 160 Figure 2. Semilogarithmic plot of the relative concentrations of naphOC under an oxygen partial pressure of 150 Torr using an oxythalene (V and V), 1-methylnaphthalene (0 and O ) , and 2-methylgen/argon gas mixture. The results of these measurements and naphthalene (+ and 0) as a function of time when added to hexadecane their comparison with results previously obtained using a stirat 160 OC autoxidizing under 760 Torr of O2 (solid symbols and lines) red-flow reactort3indicate that oxidation in the batch reactor is at to = 620 s and when added to hexadecane at 160 OC which was being bubbled with argon at the same flow rate as oxygen in the autoxidizing controlled by mass transfer of oxygen at 150 Torr though not at hexadecane experiments (open symbols and interrupted lines). The thick 760 Torr.27 For this reason, further studies at 150 Torr of 0 2 , lines are the best straight lines through the experimental points for both including studies of the effects of added (alkyl)naphthalenes, were 1- and 2-methylnaphthalene. Concentrations of the additives were not undertaken. It is hoped that an investigation of the retardation 0 . 2 7 4 3 1 M in all cases. On this plot, the time is measured from the of hexadecane autoxidation by alkylnaphthalenes will be pursued time of addition of the additive to the reaction vessel. shortly in the stirred-flow reactor. Retardation of the Autoxidation of Hexadecane by (Methyl)(seeFigure 1). This means that K (eq XI) is approximately halved naphthalene. The addition of 1- or 2-methylnaphthalene to because the diluting effect of the added (methy1)naphthalene is hexadecane which had been preoxidized at 160 O C under 760 Torr almost negligible, viz., [C16H34]= 2.98 M for the neat material of 0,caused an immediate reduction in the rate of oxidation. and 2.83 M for hexadecane containing 0.3 M (methyl)However, in contrast to BMP, such additions did not bring the naphthalene. This reduction in K is not due to any change in ki oxidation to a complete halt. Thus, addition of either 1- or because the simultaneous addition of 1.2 X M BMP and ca. 2-methylnaphthalene at the same time point as had been used for 0.3 M 1-methylnaphthalene (open circles in Figure 1) produced BMP, v ~ z . , at , ~ to = 620 s, [-0OHlb'I2 i= 0.1 MI/,, in quantities an induction period of the same length as had previously been appropriate to produce a ca. 0.3 M solution of the methylobtained by the addition of 1.2 X lo-' M BMP alone (open squares naphthalene in the oxidizing hexadecane, reduced the slope of the in Figure 1). Furthermore, because the concentration of the major line in the plot of [-OOH],'/2versus t by about a factor of 2 (see oxidizable substrate, hexadecane, is virtually unchanged by the filled circles and triangles in Figure 1). This reduction in K must addition of ca. 0.3 M (methyl)naphthalene, the major chainbe attributed to oxidation chemistry specific to the naphthalene propagating reactions will remain unchanged. This means that nucleus and not to chemistry of the methyl group because an both k, and I$ will be virtually unaffected by the (methyl)essentially identical reduction in K was produced by the addition naphthalene. Since K is determined by the magnitude of ki, k,, of about the same molar concentration of naphthalene (see filled I$, and k, (see eq XI) and since the first three of these quantities diamonds in Figure 1). The plots of [-00H],1/2 versus t subwill be little affected by the addition of ca. 0.3 M (methyl)sequent to the addition of ca. 0.3 M (methy1)naphthalene at to naphthalene, it must be concluded that k, has increased, and = 620 s are approximately linear until t 2 3000 s (see Figure 1). increased by about a factor of 4. After this time, the -OOH concentration increases a t a slightly The effective rate constant for chain-termination in the presence greater rate. This increase in the rate of formation of -OOH at of ca. 0.3 M (methy1)naphthalene could increase because of the longer times may be partly or entirely due to the volatility of the following: (i) The second-order rate constant for peroxyl peroxyl (methy1)naphthalene since volatility causes a substantial loss of chain-termination reactions is increased. (ii) There is a contrithe (methy1)naphthalene after a few thousand seconds (see Figure bution from a kinetically-first-order chain-termination reaction. 2) -28 (iii) Both of the above phenomena occur. The addition of ca. 0.3 M (methy1)naphthalene to hexadecane With regard to possibility i, 2k, has a value of about 1.12 X preoxidized under 760 Torr of O2to [-OOH], = 0.01 M and to lo8 M-' s-I a t 160 0C,20,21 which is well below the upper limit of = 620 s25 roughly halves the slope of the [-OOH],1/2versus t plot ca. 5.3 X lo9 M-' s-' which we calculate29for a radical radical reaction which proceeds a t the diffusion-controlled limit in hex(25) In these and analogous experiments a sample of hexadecane was adecane at this temperature. If, therefore, these (methyl)removed from the reactor at 600 s and was titrated to measure [+OH],which naphthalene retarded hexadecane autoxidations could be properly M. Materials were vaned from a low of 7.7 X IO-' M to a high of 11.3 X described by eqs IX and XI, i.e., if chain-termination were entirely added to the reactor 20 s later. Note that all concentrations have been a second-order process, then we can put limits on the (methyl)corrected for the change in density with temperature and hence are actual concentrations at 160 "C. naphthalene modulated value of K, hereafter referred to as K'. (26) Horswill, E. C.; Howard, J. A.; Ingold, K.U. Cum J . Chrm. 1966, These limits are (1.12/53)'12K = 0.15K < K'< K. 44, 985-991. For the experiments described above (viz., addition of ca. 0.3 (27) For the autoxidation of neat hexadecane at 160 OC,4 is calculated M (methy1)naphthalene at [-OOH],, = 0.01 M, to = 620 s, 760 to be equal to 1.28 at 150 Torr of O2 from data obtained in the stirred-flow reactor." The results obtained in the batch reactor used in the present study Torr of 0,) we find a 2-fold decrease in rate, Le., K' = 0.5K. would have implied a much smaller value for 4 at 150 Torr of 02. Therefore, it is not essential to invoke a kinetically-first-order (28) The decrease in the concentration of naphthalene, in particular, is so chain-termination process (possibility ii). However, such a substantial after 3000 s that an even more significant deviation from linearity first-order process must be invoked in order to account for the of the [-00H],'/2 vs I plot for this additive might have been expected. We suggest that the rate accelerating effect caused by volatility of the (methretardation which is observed when higher concentrations of
\\\
i
+
+
y1)naphthalene is partially compensated for in the plots shown in Figure 1 by the fact that some (methy1)naphthalene oxidation products are more potent retarders of autoxidation than the parent hydr~carbons.~ These retarders are probably (methy1)naphthoquinones.'
(29) Estimated from data given in: Schuh, H.-H.; Fisher, H. Hela Chim. Acto 1978, 62,2130-2164.
7730 J. Am. Chem. SOC.,Vol. 114, No. 20, 1992
0.0
I/
,
,
,
(
,
,
,
/
(
,
,
,
,
2000
0
Time
I
,
/
,
,
, I , , , ,
4000
I
, , , ,
1
6000
s
H'
'm
Figure 3. Plot of [hydroperoxide]
vs time for the self-initiated autoxidation of hexadecane a t 160 OC under 760 Torr of 02:no additives (D); with additive, 1-methylnaphthalene at concentrations of 0.15 (e), 0.31 ( O ) , 0.61 (A),and 1.06 (V). The 1-methylnaphthalene was introduced into the autoxidizing hexadecane a t to = 620 s (680 s for the highest concentration) and [-OOH], = 0.01 M. The curves shown for the 1-methylnaphthalene modulated autoxidation of hexadecane, corresponding to the above concentrations of 1-methylnaphthalene, have been computed as described in the text.
(methy1)naphthalene are added under similar experimental conditions. For example, the slope of the straight line which can be drawn through the experimental points for a plot of [-00H],1/2 versus t for an experiment in which 1.06 M 1-methylnaphthalene was added to preoxidized hexadecane at 160 OC under 760 Torr of 02 ([-OOH],, 0.01 M, t o = 680 s, [C16H34],, = 2.45 M, see Figure 3) yields K'= 0.10Kwhich is lower than the limiting value of 0.15K. First-order chain termination is also required to explain the very strong initial retardation observed when (methyl)naphthalene is added to hexadecane which has not been preoxidized (vide infra). Despite the foregoing, the agreement between calculated and experimental data is not acceptable if a kinetically-first-order chain-termination process is introduced into a kinetic model in which the magnitude of the second-order rate constant for chain-termination remains invariant and equal to 2k,. Possibiiities i and ii can therefore be ruled out. Possibility iii provides a very satisfactory degree of agreement between theory and experiment with a kinetic model which includes both a first-order chain-termination and a second-order chain-termination for which the rate constant increases as the concentration of (methy1)naphthaleneincreases. These two requirements can be accommodated within a relatively simple reaction scheme, Scheme 11. In Scheme 11, NpCH3 represents methylnaphthalene, NpCH2' the naphthylmethyl radical, r 00' represents all organic peroxyl radicals present in the system, i.e., r o o ' = x(C16H330@ + HOOC16H&0' NpCH200'), and -00'represents all the peroxyl radicals present, i.e., -00' = x ( r O O * + HOO'). This scheme combines the main features of Scheme I with many of the features shown in a scheme in the preceding p a ~ e r . ~ , ~We O attribute the increase in the second-order rate constant for
+
roo' + Hoo'
+
- 4 -H 2 4 + 4
Hoo'
concentrations (-[-OOH]) generated by hexadecane autoxidation are very much lower (typically ca. 0.01-0.05 M) than the concentrations of Me3C00H which were added earlier (21.0 M). As a consquence, the quantitative conversion of HOO' into Me,COO' via the reaction HOO' + Me3COOH HOOH + Me3COO' has no parallel in the current experiments, is., reaction -24 is of much less importance than the other reactions which consume HOO', viz., reactions 15, 26, and 27 in particular. It should also be noted that the 'nonradical and non-hydroperoxidic product" from reactions 21.23, and 25 refers only to the absence of hydroperoxide formation from the -00 or r 00 moiety. If the reaction in question involves the H00Cl,H3200moiety then, of course, hydroperoxide-containing products will result. However, the concentration of hydroperoxide in the system will not change.
-
(26) (27)
chain-termination to the interaction of HOO' radicals in cross (reaction 26) and self (reaction 27) radical + radical reactions. The HOO' radicals are formed via reactions 19 and 22, so their rate of formation and, hence, the enhancement in the overall second-order rate constant for chain-termination increases with an increase in the (methy1)naphthalene concentration and oxygen partial pressure. We attribute the kinetically-first-order chaintermination, as before: to peroxyl radical trapping by (methy1)naphthoxyl radicals (reaction 21) which are themselves produced by decomposition of the peroxycyclohexadienyl radical (reaction 20) formed by peroxyl addition to the (methyl)naphthalene (reaction 19). Computer Simulation of the (Methy1)naphthalene Retarded Autoxidation of Hexadecane. A kinetic analysis of Scheme I1 is given as an Appendix in which it is shown that
(kt66 (30) In comparing the present Scheme I1 with the earlier Scheme in ref 4 used to describe the Me3COOH modulated autoxidation of methylnaphthalene at much lower temperatures, it should be noted that the r OOH
a +
r
+ k27)[H00*I2- ki[-OOH]
(XII)
where 6 = [rO@]/[HOO*]. It is also shown in the Appendix that the HOW radical concentration can be represented by [HOO'I = [+ig[Np(CH3)18
+
. \ / ( ~ I ~ [ N P ( C H ~ )+ I S8ki[-00Hl12k2562 )~ + 2k266 + 2k27)]/ 2(2k2s62 2k266+ 2k2,j (XIII)
+
where /3 = (2f+ 2fs) a n d f = k20/(k20+ k 2 2 [ 0 2 ] ) . From earlier work values of k I 5 k16r , k25,k26r k27r ki, and 4 at 160 OC (see Table I) are known or can be estimated on the basis of the assumptions indicated in this table.4J832+22*29,31-40 Of the
J . Am. Chem. SOC.,Vol. 114, No. 20, 1992 1131
Autoxidation of Alkylnaphthalenes. 2 Table I. Kinetic Parameters for the (Methy1)naphthalene Modulated Autoxidation of Hexadecane at 160 OC parameter assumption this assumes Since k, is k15= k, = 88.9 M-'s-' that all peroxyl radicals in the system have equal reactivity in intermolecular H-atom abstractions. Even if this assumption is not entirely valid," the approximation is reasonable since the major abstracting species will be the hexadecylperoxyl radicals under all conditions. Based on a value obtained by extrapolation of our low-temperature kinetic data4 for the reaction: N p C H 2 0 0 ' + NpCH3 NpCHzOOH + NpCH2m.36 kZ5= k, = 5.6 X lo7 M-I s-l Since k, is known20*21this assumes that the N p C H 2 0 0 ' radicals react with the hexadecylperoxyl radicals and with themselves with the same rate constant as two hexadecylperoxyls. +
k26 2.5 X lo9 M-I s-' kZ7= 2.5 X lo9 M-I s-l
It is assumed that k26 = k27. This reaction is assumed37 to be diff~sion-controlled~~ in hexadecane a t this temperature, viz., 2k2, = 5 X
109 M-1
ki = 2.82 x 10-5 S-I 4
s-1.
See refs 12 and 13. Calculated2* for the hexadecane concentration present in each run after addition of the (methy1)naphthalene using an oxygen concentration of 2.65 X lo-' M,i.e., the concentration appropriate for 760 Torr of 02.22*23
remaining three unknowns in eqs XI1 and XIII, one, k19, is a constant, ~ n e , f ( = k , ~ / ( k+~k22[02])), ~ varies only with a change in the oxygen pressure, and one, 6 (=[r00.]/[H00*]), depends primarily on the [C16H34]/[Np(CH3)]ratio. This last quantity, (31) In this connection, the limited evidence available suggests that the HOO' radical does have about the same reactivity in hydro en atom abstraction as a secondary alkylperoxyl radical. For example:@ per reactive (bis-allylic) hydrogen atom the rate constant for H-atom abstraction, k/H, from 1,4-cyclohexadiene by HOO' has been reported to be 85 M-l s-' in n-decane at 30 0C'3 and 40 M-I s-] in water at 25 OC,)) while for abstraction of a bis-allylic H-atom from a polyunsaturated fatty acid by the corresponding secondary alkylperoxyl, k / H = 45 M-I s-I at 30 0C.35 (32) For a comprehensive listing of rate constants for reactions involving peroxyl radicals including the HOO' radical, see: Howard, J. A.; Scaiano, J. C. Radical Reaction Rates in Liquids; Landolt-Barnstein, New Series. Springer-Verlag: Berlin, 1984;Vol. 13d, pp 193-422. (33) Howard, J. A.; Ingold, K. U. Can. J . Chem. 1967, 45, 785-792. (34) Sawyer, D. T.;McDowell, M.S.;Yamaguchi, K. S. Chem. Res. Toxicol. 1988, I, 97-100. (35) Howard, J. A.; Ingold, K. U. Can. J . Chem. 1967, 45, 793-802. (36) Note that the hydrogen atoms in the methyl group of the methylnaphthalenes are, as expected, more readily abstracted by an attacking peroxyl radical than the secondar , parafinic hydrogen atoms in hexadecane, i.e., k,6/H 3413 = 11.3 M-'s-' vs kll/H 88.9128 = 3.2 M-'S-'. (37) Values reported for k2, are very much greater in non lar solvents k ~3.5 , X (and in the gas phase) than in polar solvent^.'^ For e ~ a m p l e , ~ = lo9,2.8 X lo9,3.4 X lo8,and 3.2X lo8 M-I s-l at 30 'C in CCl,/fluorolube (qWc = 8.0 cP), CCI,, n-decane, and chlorobenzene, respectively (and 1.5 X 1O'O M-' s-I in the gas phase),'* whereas its value is 2.2 X lo6 M-l s-I a t 30 at room temperature in water.)'^'^ OC in acetonitrile" and ca. 1 X 106 M-I (The reaction in the gas phase is known to yield H202and 0 2 only.)40 (38) See,e.g.: Burgess, R. H.; Robb, J. C. Chem. Soc. London,Spec. Publ. 1958, 9, 167. (39) See, e.g.: Bielski, B. H. J.; Saito, E. J. Phys. Chem. 1962, 66, 2266-2268. Czapski, G.; Bielski, B. H. J. J. Phys. Chem. 1963, 67, 2180-2184. Currie, D. J.; Dainton, F. S. Tram. Furaday SOC. 1965, 61, 1156-1 165. Adams, G. E.;Boag, J. W.; Michael, B. D. Proc. R. Soc. London 1966, 289A, 321-341. (40) Ingold, K. U.J . Phys. Chem. 1988, 92, 4568-4569.
6, is expected to change only rather slowly during an oxidation. It will change because of evaporative losses of the (methyl)naphthalene and because reactions 24 and -24 come to play an increasingly important role as the hydroperoxide concentration increases. With regard to the latter potential cause for a change in 6 during a reaction, it should be noted that immediately following the (methy1)naphthalene addition the concentration of hydrogen peroxide is extremely low (ca. 4 4 % of the total [OOH])41and therefore reaction 24 can be ignored. At this point under typical experimental conditions, Le., to = 620 s, the [-HI concentration is ca. 0.01 M and so reaction -24 does occur to a small extent. That is, we estimate43that k24 = k-24 = 5.4 X lo3 M-I s-I at 160 OC and hence the ratio of HOO' radicals which react by H-atom abstraction from 0.01 M [*OH] relative to those which abstract hydrogen from 2.8 M hexadecane is only ( 5 X lo3) X 0.01/89X 2.8 = 0.2. The [-OH] concentration must therefore rise to ca. 0.05 M before reactions -24 and 15 become equally important as routes for the conversion of HOO' into r 00' radicals. Because eq XI1 is not readily integrated, a computer simulation was used to calculate [-OOH] as a function of time using the approximation A[-OOH] At
d[-OOH] dt
(XIV)
which will be valid for small At. For these simulations Ar = 1 s was used since smaller values of At had little effect on the results. The program calculated the accumulation of hydroperoxidic oxidation products on the basis of the kinetic analysis given above and the rate constants given in Table I and its associated footnotes. The assumption is made that [C16H34]and [02] do not change during the course of an experiment. However, it is known (see Figure 2) that the (methy1)naphthalene concentration declines during an experiment due to both evaporation and reaction. The [Np(CH3)] concentration was therefore estimated as a function of time by interpolation using the data presented in Figure 2. To simplify the computational procedure a preliminary estimate of 6 (=[rOO*]/[HOO*]) was made under each initial set of experimental conditions as described below. The ratio, a, of the rates of formation of rOO' and HOO' radicals is given by
This equation indicates that a >> 1 under all conditions. If we now neglect the first-order chain-termination reactions then, because a >> 1, we can make the simplifying assumption that HOO' radicals are destroyed in the very fast, bimolecular, HOO' + r 00'cross-reaction (reaction 26) and that the large fraction of rOO' radicals which remain are lost by their much slower bimolecular self-reaction (reaction 25). The ratio, b, of the rates of destruction of rOO' and HOO' radicals can therefore be approximated by
b=
2kz5[rOO*]* k2,[r00'][HOO']
Since the rates of formation and destruction of the peroxyl radicals ~~~
(41) Although there are several potential sources of the HOO' radical, and hence of H202,in autoxidizing hexadecane, the major route probably involves the further oxidation of the alcohol products formed via the Russell termination of two sec-alkylperoxyl radical^.'^ (42) Niu, Q.J.; Mendenhall, G. D. J. Am. Chem. Soc. 1992,114,165-172. (43) Based on Arrenhius equation given for the reaction of rerr-butylperoxy1 radicals with tetralin hydroperoxide." We also note that this Arrhenius equation" yields k = 1.4X IO3 M-l s-I at 70 OC, at which temperature the rate constant for the reaction C6H5CH(CH3)OO'+ H202 C&&H(CH3)OOH HOO' has been estimated to have essentially the same value, viz.$J 1.56 X 10' M-' s-l (44) Chenier, J. H.B.;' Howard, J. A. Can. J . Chem. 1975, 53, 623-627. (45) Gol'denburg, V.I.; Denisov, E. T.; Ennakova, N. A. Izu. Akad. Nauk SSSR, Ser. Khim. 1990,738-743.
+
-
Igarashi et al.
7732 J. Am. Chem. SOC.,Vol. 114, No. 20, 1992 must, according to the normal steady-state assumption, be equal, we have
An
t t
\ 0.3
That is
Equation XVIII becomes more reliable as the (methy1)naphthalene concentration is reduced and as the oxygen pressure is increased, Le., under conditions where [HOO’]
